Yeah, I didn't say work hard on weekends, but rather, work smarter, take 2-3 hours to review things, advance things etc. Of course if you're the guy who can "save the demo" by working 18h straight on a weekend it helps too.
And of course, never work for free. Even those extra weekend hours, make sure you get paid for them. This is a huge part on getting and maintaining respect from your employer.
Fully remote worker (from another country) on a leadership position here.
Hard work and exceptional availability and communication skills. I was the guy who would work weekends, be the first the show up online etc. Never procrastinate. Keep track of other people's work and make your efforts in moving things forward crystal clear to your boss. Deliver.
People are not going to bet on a remote worker for displaying exceptional commitment or leadership skills. You have to actively display them yourself, but not in a pushy manner. Just be the absolute most useful and reliable person you can be. Soon enough you'll have enough responsibilities and involvement in projects that a leadership role will emerge naturally.